Topics in quaternion linear algebra / Leiba Rodman.

Format:

Book

Author/Creator:

Rodman, L., author.

Series:

Princeton series in applied mathematics.

Princeton Series in Applied Mathematics

Language:

English

Subjects (All):

Algebras, Linear--Textbooks.

Algebras, Linear.

Quaternions--Textbooks.

Quaternions.

Physical Description:

1 online resource (379 p.)

Edition:

Course Book

Place of Publication:

Princeton, New Jersey ; Oxfordshire, England : Princeton University Press, 2014.

Language Note:

English

Summary:

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Contents:

Front matter

Contents

Preface

Chapter One. Introduction

Chapter Two. The algebra of quaternions

Chapter Three. Vector spaces and matrices: Basic theory

Chapter Four. Symmetric matrices and congruence

Chapter Five. Invariant subspaces and Jordan form

Chapter Six. Invariant neutral and semidefinite subspaces

Chapter Seven. Smith form and Kronecker canonical form

Chapter Eight. Pencils of hermitian matrices

Chapter Nine. Skewhermitian and mixed pencils

Chapter Ten. Indefinite inner products: Conjugation

Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution

Chapter Twelve. Mixed matrix pencils: Nonstandard involutions

Chapter Thirteen. Indefinite inner products: Nonstandard involution

Chapter Fourteen. Matrix equations

Chapter Fifteen. Appendix: Real and complex canonical forms

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781400852741

1400852749

OCLC:

881568749